Abstract
We present a simple to implement and efficient pseudorandom generator based on the factoring assumption. It outputs more than pn/2 pseudorandom bits per p exponentiations, each with the same base and an exponent shorter than n/2 bits. Our generator is based on results by Håstad, Schrift and Shamir [HSS93], but unlike their generator and its improvement by Goldreich and Rosen [GR00], it does not use hashing or extractors, and is thus simpler and somewhat more efficient. In addition, we present a general technique that can be used to speed up pseudorandom generators based on iterating one-way permutations. We construct our generator by applying this technique to results of [HSS93]. We also show how the generator given by Gennaro [Gen00] can be simply derived from results of Patel and Sundaram [PS98] using our technique.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
W. Alexi, B. Chor, O. Goldreich, and C. Schnorr. RSA and Rabin functions: Certain parts are as hard as the whole. SIAM Journal on Computing, 17(2):194–209, April 1988.
L. Blum, M. Blum, and M. Shub. A simple unpredictable pseudo-random number generator. SIAM Journal on Computing, 15(2):364–383, May 1986.
M. Blum and S. Micali. How to generate cryptographically strong sequences of pseudo-random bits. SIAM Journal on Computing, 13(4):850–863, November 1984.
Rosario Gennaro. An improved pseudo-random generator based on discrete log. In Mihir Bellare, editor, Advances in Cryptology-CRYPTO 2000, volume 1880 of Lecture Notes in Computer Science, pages 469–481. Springer-Verlag, 20-24 August 2000.
Oded Goldreich. Foundations of Cryptography: Basic Tools. Cambridge University Press, 2001.
Oded Goldreich and Vered Rosen. On the security of modular exponentiation with application to the construction of pseudorandom generators. Technical Report 2000/064, Cryptology e-print archive, http://eprint.iacr.org, 2000. Prior version appears in [Ros01].
J. Håstad, A. W. Schrift, and A. Shamir. The discrete logarithm modulo a composite hides O(n) bits. Journal of Computer and System Sciences, 47:376–404, 1993.
Chae Hoon Lim and Pil Joong Lee. More flexible exponentiation with precomputation. In Yvo G. Desmedt, editor, Advances in Cryptology-CRYPTO’ 94, volume 839 of Lecture Notes in Computer Science, pages 95–107. Springer-Verlag, 21–25 August 1994.
S. Patel and G. Sundaram. An efficient discrete log pseudo random generator. In Hugo Krawczyk, editor, Advances in Cryptology-CRYPTO’ 98, volume 1462 of Lecture Notes in Computer Science, pages 304–317. Springer-Verlag, 23-27 August 1998.
Vered Rosen. On the security of modular exponentiation with application to the construction of pseudorandom generators. Technical Report TR01-007, ECCC (Electronic Colloquium on Computational Complexity, http://www.eccc.uni-trier.de/eccc), 2001.
A. C. Yao. Theory and application of trapdoor functions. In 23rd Annual Symposium on Foundations of Computer Science, pages 80–91, Chicago, Illinois, 3–5 November 1982. IEEE.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dedić, N., Reyzin, L., Vadhan, S. (2003). An Improved Pseudorandom Generator Based on Hardness of Factoring. In: Cimato, S., Persiano, G., Galdi, C. (eds) Security in Communication Networks. SCN 2002. Lecture Notes in Computer Science, vol 2576. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36413-7_7
Download citation
DOI: https://doi.org/10.1007/3-540-36413-7_7
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-00420-2
Online ISBN: 978-3-540-36413-9
eBook Packages: Springer Book Archive